Groups, Geometry, and Dynamics

Magnus intersections of one-relator free products with small cancellation conditions

Arye Juhász[1]

(1) Technion - Israel Institute of Technology, Haifa, Israel

Donald Collins initiated the study of intersections of Magnus
subgroups in one-relator groups. In particular, he characterized
those intersections of Magnus subgroups that are not Magnus
subgroups. In the present work we show that Collins’ results extend
to one-relator quotients of free products of groups with a small
cancellation condition and give a complete list of those defining
relators for which Magnus subgroups do not intersect in a Magnus
subgroup. We use van Kampen diagrams and word combinatorics.